Quantifying the post-earthquake functional recovery of railway stations presents significant challenges.This paper first establishes a post-earthquake function calculation method for railway stations,encompassing the ...Quantifying the post-earthquake functional recovery of railway stations presents significant challenges.This paper first establishes a post-earthquake function calculation method for railway stations,encompassing the establishment of relationships between the station’s function and the damage state,function loss,and failure probability of components and professional equipment in each layer.Also,the“4 stages-6 sequences”post-earthquake repair method is present,taking into account the functional and structural characteristics of railway stations.Additionally,a novel piecewise function for the post-earthquake functional dynamic recovery of railway stations is developed.A case study is conducted on a typical railway station to demonstrate the analysis procedure.Results indicate that under fortification,rare,and extremely rare earthquake scenarios,the interlayer drift ratio(IDR)of the railway station were 1/276,1/143,and 1/52,respectively,and corresponding peak floor acceleration(PFA)were 6.31 m/s^(2),7.82 m/s^(2),and 8.57 m/s^(2),respectively.The post-earthquake function of the railway station was 93.21%,82.33%,and 64.16%of its initial function.The repair times were 6.66 days,18.65 days,and 37.42 days.The displacement-sensitive,non-structural components were identified as the most vulnerable to damage.And the first repair stage(R_(1))which was mainly used to repair structural components and non-structural transport components,accounted for the highest proportion of total repair time.展开更多
This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the acc...This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.展开更多
This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulat...This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.展开更多
Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instr...Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instrument function,is measured in X-ray Thom-son scattering(XRTS)experiments,which allow the study of electronic structure properties at the microscopic level.Among the various ab initio methods,linear-response time-dependent density-functional theory(LR-TDDFT)is a key framework for simulating the DSF.The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation.A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases,making LR-TDDFT impractical for modeling XRTS measurements over large energy scales,such as in backward scattering geometry.In this work,we consider and test an alternative approach to LR-TDDFT that employs the Liouville–Lanczos(LL)method for simulating the DSF of WDM.This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed.We compare the results obtained from the LL method with those from the solution of Dyson’s equation using the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen.Additionally,we utilize exact path integral Monte Carlo results for the imaginary-time density-density correlation function(ITCF)of warm dense hydrogen to rigorously benchmark the LL approach.We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers,the effects of pseudopotentials,and the role of Lorentzian smearing.The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape,supporting experimental efforts and advancing WDM theory.展开更多
The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients....The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.展开更多
Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the...Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.展开更多
Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to n...Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.展开更多
Layered intercalated functional materials of layered double hydroxide type are an important class of functional materials developed in recent years. Based on long term studies on these materials in the State Key Labor...Layered intercalated functional materials of layered double hydroxide type are an important class of functional materials developed in recent years. Based on long term studies on these materials in the State Key Laboratory of Chemical Resource Engineering in Beiiing University of Chemical Technology, the orinciole for the design of controlled intercalation processes in the light of tuture production processing requirements has been developed. Intercalation assembly methods and technologies have been invented to control the intercalation process for preparing layered intercalated materials with various structures and functions.展开更多
We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. M...We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.展开更多
We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to thi...We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.展开更多
A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(F...A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.展开更多
The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the meth...The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the method of lines (MOL) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretize the governing equation into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs. The functions of thermal properties are directly embodied in these equations and these properties are not discretized in the domain. Thus, difficulty of FEM and BEM is overcome by the method. As a numerical example, the temperature field of a plane problem is analyzed for FGMs through varying thermal conductivity coefficient by the MOL.展开更多
Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs...Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.展开更多
[Objectives] This study was conducted to investigate the drying methods,functional and structure properties of dietary fiber( DF) from peanut shells.[Methods]Peanut shells were used as a raw material to prepare peanut...[Objectives] This study was conducted to investigate the drying methods,functional and structure properties of dietary fiber( DF) from peanut shells.[Methods]Peanut shells were used as a raw material to prepare peanut shell dietary fiber( DF) by hot air drying( HA) and vacuum freeze drying( VF),respectively,and their functional and structural characteristics were compared in detail. [Results]The solubility,water holding capacity,oil holding capacity and swelling capacity of HA-DF and VF-DF were 2. 15 %,7. 63 g/g,7. 73 g/g,10. 35 ml/g and 3. 85 %,14. 98 g/g,15. 25 g/g,15. 85 ml/g,respectively. The total phenol contents were 2. 623 and 5. 173 mg GAE/g,respectively. The IC(50) values of ·OH,O2^-· and DPPH free radicals were 4. 16 and 4. 09 mg/ml,7. 90 and 3. 32 mg/ml,and 3. 19 and 3. 09 mg/ml,respectively. The molecular weight of VF-DF was smaller,and it had narrow molecular weight distribution and denser particles. Electron microscopy showed that VF-DF had a porous network like honeycomb and swelled structure. [Conclusions]This study can provide a theoretical basis for the functional modification and comprehensive utilization of peanut shell dietary fiber.展开更多
Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes in...Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.展开更多
Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-m...Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-material interfaces are classified based on discontinuity degrees of their material properties and their derivatives at the interfaces. Numerical results indicate that discontinuity exerts remarkable effect on the temperature profile and stress value at the interface of two bonded functionally-graded materials. Under the thermal flux loading conditions, the stronger the interface discontinuity is, the smaller the heat flux is.展开更多
In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on t...In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on the high-order theory of transverse vibration of circular cross-section beams,lateral displacement equation was reconstructed neglecting circumferential shear stress.Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue.Then,differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue problems.Natural frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time,and corresponding modal functions were solved together.The obtained numerical results indicated that the natural frequencies of functionally graded(FG)circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related literatures.In addition,influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous studies.Numerical results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.展开更多
In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a s...In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.展开更多
The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES...The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.展开更多
Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is d...Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.展开更多
基金National Natural Science Foundation of China under Grant No.52278534the Sichuan Provincial Natural Science Foundation of China under Grant No.2022NSFSC0423。
文摘Quantifying the post-earthquake functional recovery of railway stations presents significant challenges.This paper first establishes a post-earthquake function calculation method for railway stations,encompassing the establishment of relationships between the station’s function and the damage state,function loss,and failure probability of components and professional equipment in each layer.Also,the“4 stages-6 sequences”post-earthquake repair method is present,taking into account the functional and structural characteristics of railway stations.Additionally,a novel piecewise function for the post-earthquake functional dynamic recovery of railway stations is developed.A case study is conducted on a typical railway station to demonstrate the analysis procedure.Results indicate that under fortification,rare,and extremely rare earthquake scenarios,the interlayer drift ratio(IDR)of the railway station were 1/276,1/143,and 1/52,respectively,and corresponding peak floor acceleration(PFA)were 6.31 m/s^(2),7.82 m/s^(2),and 8.57 m/s^(2),respectively.The post-earthquake function of the railway station was 93.21%,82.33%,and 64.16%of its initial function.The repair times were 6.66 days,18.65 days,and 37.42 days.The displacement-sensitive,non-structural components were identified as the most vulnerable to damage.And the first repair stage(R_(1))which was mainly used to repair structural components and non-structural transport components,accounted for the highest proportion of total repair time.
基金supported by the Advance Research Project of Civil Aerospace Technology(Grant No.D020304)National Nat-ural Science Foundation of China(Grant Nos.52205257 and U22B2083).
文摘This paper proposes a new step-by-step Chebyshev space-time spectral method to analyze the force vibration of functionally graded material structures.Although traditional space-time spectral methods can reduce the accuracy mismatch between tem-poral low-order finite difference and spatial high-order discre tization,the ir time collocation points must increase dramatically to solve highly oscillatory solutions of structural vibration,which results in a surge in computing time and a decrease in accuracy.To address this problem,we introduced the step-by-step idea in the space-time spectral method.The Chebyshev polynomials and Lagrange's equation were applied to derive discrete spatial goverming equations,and a matrix projection method was used to map the calculation results of prev ious steps as the initial conditions of the subsequent steps.A series of numerical experiments were carried out.The results of the proposed method were compared with those obtained by traditional space-time spectral methods,which showed that higher accuracy could be achieved in a shorter computation time than the latter in highly oscillatory cases.
基金supported in part by the National Natural Science Foundation of China(62473221)the Natural Science Foundation of Shandong Province,China(ZR2024MF006)Qingdao Natural Science Foundation(24-4-4-zrjj-165-jch)。
文摘This paper is concerned with event-triggered control of discrete-time systems with or without input saturation.First,an accumulative-error-based event-triggered scheme is devised for control updates.When the accumulated error between the current state and the latest control update exceeds a certain threshold,an event is triggered.Such a scheme can ensure the event-generator works at a relatively low rate rather than falls into hibernation especially after the system steps into its steady state.Second,the looped functional method for continuous-time systems is extended to discrete-time systems.By introducing an innovative looped functional that links the event-triggered scheme,some sufficient conditions for the co-design of control gain and event-triggered parameters are obtained in terms of linear matrix inequalities with a couple of tuning parameters.Then,the proposed method is applied to discrete-time systems with input saturation.As a result,both suitable control gains and event-triggered parameters are also co-designed to ensure the system trajectories converge to the region of attraction.Finally,an unstable reactor system and an inverted pendulum system are given to show the effectiveness of the proposed method.
基金supported by the Center for Advanced Systems Understanding(CASUS),financed by Germany’s Federal Ministry of Education and Research(BMBF)and the Saxon State Government out of the State Budget approved by the Saxon State Parliamentfunding from the European Research Council(ERC)under the European Union’s Horizon 2022 research and innovation programme(Grant Agreement No.101076233,“PREXTREME”)funding from the European Union’s Just Transition Fund(JTF)within the project Röntgenlaser-Optimierung der Laserfusion(ROLF),Contract No.5086999001,co-financed by the Saxon State Government out of the State Budget approved by the Saxon State Parliament.
文摘Ab initio modeling of dynamic structure factors(DSF)and related density response properties in the warm dense matter(WDM)regime is a challenging computational task.The DSF,convolved with a probing X-ray beam and instrument function,is measured in X-ray Thom-son scattering(XRTS)experiments,which allow the study of electronic structure properties at the microscopic level.Among the various ab initio methods,linear-response time-dependent density-functional theory(LR-TDDFT)is a key framework for simulating the DSF.The standard approach in LR-TDDFT for computing the DSF relies on the orbital representation.A significant drawback of this method is the unfavorable scaling of the number of required empty bands as the wavenumber increases,making LR-TDDFT impractical for modeling XRTS measurements over large energy scales,such as in backward scattering geometry.In this work,we consider and test an alternative approach to LR-TDDFT that employs the Liouville–Lanczos(LL)method for simulating the DSF of WDM.This approach does not require empty states and allows the DSF at large momentum transfer values and over a broad frequency range to be accessed.We compare the results obtained from the LL method with those from the solution of Dyson’s equation using the standard LR-TDDFT within the projector augmented-wave formalism for isochorically heated aluminum and warm dense hydrogen.Additionally,we utilize exact path integral Monte Carlo results for the imaginary-time density-density correlation function(ITCF)of warm dense hydrogen to rigorously benchmark the LL approach.We discuss the application of the LL method for calculating DSFs and ITCFs at different wavenumbers,the effects of pseudopotentials,and the role of Lorentzian smearing.The successful validation of the LL method under WDM conditions makes it a valuable addition to the ab initio simulation landscape,supporting experimental efforts and advancing WDM theory.
基金Project supported by the National Natural Science Foundation of China(No.11672008)
文摘The asymptotic development method is applied to analyze the free vibration of non-uniform axially functionally graded(AFG) beams, of which the governing equations are differential equations with variable coefficients. By decomposing the variable flexural stiffness and mass per unit length into reference invariant and variant parts, the perturbation theory is introduced to obtain an approximate analytical formula of the natural frequencies of the non-uniform AFG beams with different boundary conditions.Furthermore, assuming polynomial distributions of Young's modulus and the mass density, the numerical results of the AFG beams with various taper ratios are obtained and compared with the published literature results. The discussion results illustrate that the proposed method yields an effective estimate of the first three order natural frequencies for the AFG tapered beams. However, the errors increase with the increase in the mode orders especially for the cases with variable heights. In brief, the asymptotic development method is verified to be simple and efficient to analytically study the free vibration of non-uniform AFG beams, and it could be used to analyze any tapered beams with an arbitrary varying cross width.
基金Project supported by the China Postdoctoral Science Foundation(No.2018M630167)
文摘Large deformation of a cantilever axially functionally graded (AFG) beam subject to a tip load is analytically studied using the homotopy analysis method (HAM). It is assumed that its Young’s modulus varies along the longitudinal direction according to a power law. Taking the solution of the corresponding homogeneous beam as the initial guess and obtaining a convergence region by adjusting an auxiliary parameter, the analytical expressions for large deformation of the AFG beam are provided. Results obtained by the HAM are compared with those obtained by the finite element method and those in the previous works to verify its validity. Good agreement is observed. A detailed parametric study is carried out. The results show that the axial material variation can greatly change the deformed configuration, which provides an approach to control and manage the deformation of beams. By tailoring the axial material distribution, a desired deformed configuration can be obtained for a specific load. The analytical solution presented herein can be a helpful tool for this procedure.
文摘Generalized functional separation of variables to nonlinear evolution equations is studied in terms of the extended group foliation method, which is based on the Lie point symmetry method. The approach is applied to nonlinear wave equations with variable speed and external force. A complete classification for the wave equation which admits functional separable solutions is presented. Some known results can be recovered by this approach.
基金Supported by the National Key Technologies R＆D Program （2011BAE28B01） and the National Natural Science Foundation of China （21276016）.
文摘Layered intercalated functional materials of layered double hydroxide type are an important class of functional materials developed in recent years. Based on long term studies on these materials in the State Key Laboratory of Chemical Resource Engineering in Beiiing University of Chemical Technology, the orinciole for the design of controlled intercalation processes in the light of tuture production processing requirements has been developed. Intercalation assembly methods and technologies have been invented to control the intercalation process for preparing layered intercalated materials with various structures and functions.
文摘We extend the differential quadrature element method (DQEM) to the buckling analysis of uniformly in-plane loaded functionally graded (FG) plates fully or partially resting on the Pasternak model of elastic support. Material properties of the FG plate are graded in the thickness direction and assumed to obey a power law distribution of the volume fraction of the constituents. To set up the global eigenvalue equation, the plate is divided into sub-domains or elements and the generalized differential quadrature procedure is applied to discretize the governing, boundary and compatibility equations. By assembling discrete equations at all nodal points, the weighting coefficient and force matrices are derived. To validate the accuracy of this method, the results are compared with those of the exact solution and the finite element method. At the end, the effects of different variables and local elastic support arrangements on the buckling load factor are investigated.
基金The project supported by National Natural Science Foundation of China under Grant No. 10371098 and the Program for New Century Excellent Talents in Universities under Grant No. NCET-04-0968
文摘We consider the functional separation of variables to the nonlinear diffusion equation with source and convection term： ut = （A（x）D（u）ux）x ＋ B（x）Q（u）, Ax ≠ 0. The functional separation of variables to this equation is studied by using the group foliation method. A classification is carried out for the equations which admit the function separable solutions. As a consequence, some solutions to the resulting equations are obtained.
基金co-supported by the National Key R&D Program of China(Nos.2018YFF01012401-05)the National Natural Science Foundation of China(No.51975243)+2 种基金Jilin Provincial Department of Education(No.JJKH20180084KJ),Chinathe Fundamental Research Funds for the Central Universities and Jilin Provincial Department of Science&Technology Fund Project,China(Nos.20170101043JC and 20180520072JH)Graduate Innovation Fund of Jilin University,China(No.101832018C184).
文摘A Coupling Magneto-Electro-Elastic(MEE)Node-based Smoothed Radial Point Interpolation Method(CM-NS-RPIM)was proposed to solve the free vibration and transient responses of Functionally Graded Magneto-Electro-Elastic(FGMEE)structures.By introducing the modified Newmark method,the displacement,electrical potential and magnetic potential of the structures under transient mechanical loading were obtained.Based on G space theory and the weakened weak(W2)formulation,the equations of the multi-physics coupling problems were derived.Using triangular background elements,the free vibration and transient responses of three numerical examples were studied.Results proved that CM-NS-RPIM performed better than the standard FEM by reducing the overly-stiff of structures.Moreover,CM-NS-RPIM could reduce the number of nodes while guaranteeing the accuracy.Besides,triangular elements could be generated automatically even for complex geometries.Therefore,the effectiveness and validity of CM-NS-RPIM were demonstrated,which were valuable for the design of intelligence devices,such as energy harvesters and sensors.
文摘The finite element method (FEM) and the boundary element method (BEM) are often adopted. However, they are not convenient to spatially vary thermal properties of functionally graded material (FGM). Therefore, the method of lines (MOL) is introduced to solve the temperature field of FGM. The basic idea of the method is to semi-discretize the governing equation into a system of ordinary differential equations (ODEs) defined on discrete lines by means of the finite difference method. The temperature field of FGM can be obtained by solving the ODEs. The functions of thermal properties are directly embodied in these equations and these properties are not discretized in the domain. Thus, difficulty of FEM and BEM is overcome by the method. As a numerical example, the temperature field of a plane problem is analyzed for FGMs through varying thermal conductivity coefficient by the MOL.
文摘Recently application of functionally graded materials（FGMs） have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.
基金Supported by Tangshan Science Project (19150204E)。
文摘[Objectives] This study was conducted to investigate the drying methods,functional and structure properties of dietary fiber( DF) from peanut shells.[Methods]Peanut shells were used as a raw material to prepare peanut shell dietary fiber( DF) by hot air drying( HA) and vacuum freeze drying( VF),respectively,and their functional and structural characteristics were compared in detail. [Results]The solubility,water holding capacity,oil holding capacity and swelling capacity of HA-DF and VF-DF were 2. 15 %,7. 63 g/g,7. 73 g/g,10. 35 ml/g and 3. 85 %,14. 98 g/g,15. 25 g/g,15. 85 ml/g,respectively. The total phenol contents were 2. 623 and 5. 173 mg GAE/g,respectively. The IC(50) values of ·OH,O2^-· and DPPH free radicals were 4. 16 and 4. 09 mg/ml,7. 90 and 3. 32 mg/ml,and 3. 19 and 3. 09 mg/ml,respectively. The molecular weight of VF-DF was smaller,and it had narrow molecular weight distribution and denser particles. Electron microscopy showed that VF-DF had a porous network like honeycomb and swelled structure. [Conclusions]This study can provide a theoretical basis for the functional modification and comprehensive utilization of peanut shell dietary fiber.
基金supported by the Key Project of the National Natural Science Foundation of China (10932006)Hebei Natural Science Foundation (2011210055)Hebei Key Basic Research Project (10963528D)
文摘Based on the fundamental dynamic equations of functionally graded material (FGM) cylindrical shell, this paper investigates the sound radiation of vibrational FGM shell in water by mobility method. This model takes into account the exterior fluid loading due to the sound press radiated by the FGM shell. The FGM cylindrical shell was excited by a harmonic line radial force uniformly distributing along the generator. The FGM shell equations of motion, the Helmholtz equation in the exterior fluid medium and the continuity equation at fluid-shell interface are used in this vibroacoustic problem. The expressions of sound radiation efficiency and sound field of the FGM shell have been derived by mobility method. Radiation efficiency, modal mobility and the directivity pattern of the sound field are solved numerically. In particular, radiation efficiency and directivity pattern with various power law index are analyzed.
基金supported by the National Natural Science Foundation of China(Nos.10902046,11032006and11121202)the Fundamental Research Funds for the Central Universities(lzujbky-2012-2)+1 种基金the Fund of Ministry of Education of the Program of Changjiang Scholars and Innovative Research Team in University(No.IRT0628)the Science Foundation of the Ministry of Education of China for Ph.D.program
文摘Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-material interfaces are classified based on discontinuity degrees of their material properties and their derivatives at the interfaces. Numerical results indicate that discontinuity exerts remarkable effect on the temperature profile and stress value at the interface of two bonded functionally-graded materials. Under the thermal flux loading conditions, the stronger the interface discontinuity is, the smaller the heat flux is.
基金supported by the National key Research and Development Plan of Ministry of Science and Technology of the People’s Republic of China(2017YFC0404903).
文摘In the current research,an effective differential quadrature method(DQM)has been developed to solve natural frequency and vibration modal functions of circular section beams along radial functional gradient.Based on the high-order theory of transverse vibration of circular cross-section beams,lateral displacement equation was reconstructed neglecting circumferential shear stress.Two equations coupled with deflection and rotation angles were derived based on elastic mechanics theory and further simplified into a constant coefficient differential equation with natural frequency as eigenvalue.Then,differential quadrature method was applied to transform the eigenvalue problem of the derived differential equation into a set of algebraic equation eigenvalue problems.Natural frequencies of the free vibrations of cylindrical beams with circular cross-sections were calculated at one time,and corresponding modal functions were solved together.The obtained numerical results indicated that the natural frequencies of functionally graded(FG)circular cylindrical beams obtained using differential quadrature method agreed with the results reported in related literatures.In addition,influences of varying gradient parameters on the modal shapes of circular cylindrical beams were found to be strongly consistent with previous studies.Numerical results further validated the feasibility and accuracy of the developed differential quadrature method in solving the transverse vibration of FG circular cross-section beams.
文摘In this paper,a semi-analytical method is presented for free vibration and buckling analysis of functionally graded(FG)size-dependent nanobeams based on the physical neutral axis position.It is the first time that a semi-analytical differential transform method(DTM)solution is developed for the FG nanobeams vibration and buckling analysis.Material properties of FG nanobeam are supposed to vary continuously along the thickness according to the power-law form.The physical neutral axis position for mentioned FG nanobeams is determined.The small scale effect is taken into consideration based on nonlocal elasticity theory of Eringen.The nonlocal equations of motion are derived through Hamilton’s principle and they are solved applying DTM.It is demonstrated that the DTM has high precision and computational efficiency in the vibration analysis of FG nanobeams.The good agreement between the results of this article and those available in literature validated the presented approach.The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of the several parameters such as neutral axis position,small scale effects,the material distribution profile,mode number,thickness ratio and boundary conditions on the normalized natural frequencies and dimensionless buckling load of the FG nanobeams in detail.It is explicitly shown that the vibration and buckling behaviour of a FG nanobeams is significantly influenced by these effects.
基金funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant number 107.02-2019.330。
文摘The main purpose of this paper is to present numerical results of static bending and free vibration of functionally graded porous(FGP) variable-thickness plates by using an edge-based smoothed finite element method(ES-FEM) associate with the mixed interpolation of tensorial components technique for the three-node triangular element(MITC3), so-called ES-MITC3. This ES-MITC3 element is performed to eliminate the shear locking problem and to enhance the accuracy of the existing MITC3 element. In the ES-MITC3 element, the stiffness matrices are obtained by using the strain smoothing technique over the smoothing domains formed by two adjacent MITC3 triangular elements sharing an edge. Materials of the plate are FGP with a power-law index(k) and maximum porosity distributions(U) in the forms of cosine functions. The influences of some geometric parameters, material properties on static bending, and natural frequency of the FGP variable-thickness plates are examined in detail.
文摘Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.
